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BOSTON (AP) — The state’s unemployment rate held steady at 6 percent in June, according to figures released Thursday by the state Office of Labor and Workforce Development, even though preliminary federal estimates show the state lost 2,600 jobs during the month.

June was the first month this year the state was reported to have lost jobs. The estimated 2,600 decline came on the heels of revised estimates from the federal Bureau of Labor Statistics that showed a gain of 5,000 jobs in May.

The state added 32,700 jobs during the first half of 2012.

The 6 percent unemployment rate, unchanged from May, remains at its lowest point since the fall of 2008. Massachusetts has been consistently below the national unemployment average during the economic downturn.

The U.S. jobless rate was 8.2 percent in June, unchanged from May.

Approximately 3,254,000 residents in Massachusetts were employed last month, while 206,900 were out of work, according to the state agency.

Among individual sectors, the construction industry took one of the biggest hits in June, losing 2,100 jobs, or 2 percent. Construction jobs have declined by 6.6 percent since the start of the year in the state.

Job losses were also reported in the leisure and hospitality, and education and health services sectors.

Slight gains were reported in the manufacturing, financial activities, and information sectors.

Different methodologies are used for calculating the unemployment rate and the monthly job estimates, according to state officials. The jobless rate is based on a household survey, while the jobs figures are calculated from a sample survey of employers.